Abstract The urban distribution system (DS) serves as a crucial link between end-users and the transmission grid, having a direct impact on the quality of power supply. However, DS is relatively more vulnerable to extreme events in comparison to the transmission network. Hence, it has been an urgent priority to enhance the resilience of DS. In recent years, the approach to enhancing DS resilience moving away from traditional load tracking of power sources to a source-grid-load-storage perspective as the structure evolution of DS caused by the high proportion of renewable generation. However, the study of load behavior on the demand side still has limitations, particularly in terms of precise modeling. Representatively, most literature consider the thermal control loads (TCL) as rigid loads or characterizes their cold load pick-up (CLPU) phenomenon as a fixed curve neglecting the dependence on the outage duration. Similarly, the time-varying, diverse, and complex nature of urban building loads under extreme conditions is seldom addressed in relevant papers. This significant deviation from real-world scenarios greatly impacts the applicability of relevant theoretical models and directly restrict the analysis of the load restoration process. Therefore, this paper conducts the following works to address the actual scenario of load restorations in DS. Firstly, the study delves into the dynamic coupling evolution law between urban time-varying loads and DS decision sequences under extreme conditions, considering both objective and subjective reasons. It accurately quantifies the complex behavior of urban building loads during the process of DS restoration in a universal and low-dimensional manner. The paper also explains the dependence of loads on DS restoration sequences, analyzing the decision-dependency characteristics of load from both subjective and objective perspectives. Secondly, the interaction between the DS and end-user decision-making constitutes a bi-level model. This paper employs the Karush-Kuhn-Tucker (KKT) conditions to solve and analyze a bi-level model that integrates the load side of the distribution network. This simplifies the model calculation while accurately identifying the optimal solution for the upper distribution network and the lower load side. Additionally, the paper proposes a data-driven modeling method and introduces a differential calculation adaptive model based on “time tag” technology and load restoration decision sequences. This adaptive model enables dynamic selection of diversified load behavior in distribution networks. Finally, the paper summarizes various indicators for evaluating the resilience of distribution networks and utilizes existing research results to compare and analyze the traditional double-layer model with the proposed adaptive model from six perspectives. The evaluation takes the system function curve of DS during the load recovery process as a starting point, allowing for an assessment of the advantages and disadvantages of the two models. Case studies shows that the lack of consideration for loads’ decision-dependency characteristics leads to the violations of node voltage and line flow, which positively correlated with penetration of TCLs and subjective driven load. Additionally, case studies also shows that the adaptive model can achieve fault restoration without affecting the resilience of the distribution network. While better protecting user privacy, it only takes 33% of the time of traditional bi-level models. Overall, this research provides valuable insights into load restoration under extreme conditions for urban DS. It provides a comprehensive analysis and optimization method ensures more efficient and effective decision-making processes. Meanwhile, the proposed method facilitates prompt decision-making without affecting the resilience of DS. Its solution time cost only accounts for 33% compared to the traditional bi-level model.
Deng Rongnan,Song Meng,Gao Ciwei等. Comparative Analysis of Distribution System Load Restoration Considering Decision-Dependent Behaviors of Customers[J]. Transactions of China Electrotechnical Society, 2024, 39(23): 7447-7462.
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2024, Vol. 39 
